Case in point: Trump's comments that U.S. District Judge Gonzalo Curiel, who was born in Indiana to Mexican immigrant parents, can't serve impartially in the Trump University case because of his Mexican heritage. Trump said Curiel is biased against him because of the real estate mogul's proposal to build a wall along the Southern border.

"Claiming a person can’t do their job because of their race is sort of like the textbook definition of a racist comment," Ryan said. "I think that should absolutely be disavowed. It’s absolutely unacceptable."

Ryan acknowledged that Trump's tone does interfere with the House GOP's efforts to focus on policy ideas this election cycle instead of personality politics.

"I do think these kinds of comments undercut these things, and I’m not even going to pretend to defend them," Ryan said. "I’m going to defend our ideas. I’m going to defend our agenda. What matters to us most is our principles and the policies that come from those principles and our ability to give the people of this country a better way forward."

Ryan is not the first Republican to criticize Trump for his remarks about Curiel, but most have not gone as far as to describe them as racist. One Republican who did is Nebraska Sen. Ben Sasse, who tweeted on Monday that "saying someone can't do a specific job because of his or her race is the literal definition of 'racism.'"

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Saying someone can't do a specific job because of his or her race is the literal definition of "racism."

Democrats are also appalled by Trump's remarks and in some cases feel they need to make amends with foreign leaders who may have taken offense.

Senate Foreign Relations ranking member Benjamin L. Cardin told reporters Tuesday that he would use a meeting with the Mexican foreign minister on Wednesday to do damage control over Trump's recent remarks about Curiel.

"It’s just outrageous. … To infer that there is a bias on his part is unacceptable," the Maryland Democrat said.